Polymerization process controller

ABSTRACT

A batch polymerization process controller using inferential sensing to determine the integral reaction heat which in turn is used to indicate the degree of polymerization of the reaction mixture batch. The system uses a reaction temperature compared with a desired temperature, and the result is used as a feedback to monitor and control the process. One version of the process controller also uses a feedforward signal which is an integral reaction heat indication from a process model. In another version of the process controller, the integral reaction heat is compared with a desired integral reaction heat, and result is used as another feedback to monitor and control the process. Heat production and reaction temperature profiles may be used, along with the thermokinetic equations to determine the polymerization process and reactor models which are utilized by the process controller to optimize the polymerization process in terms of efficient use of cooling water and desired polymerization of each mixture batch.

BACKGROUND

The invention pertains to polymerization reactions, particularly tomonitor and control the rate and the amount of conversion in suchreactions. More particularly, the invention pertains to accuratelydetermining the rate and amount of conversion at a particular moment ina polymerization reaction so as to control the rate of conversion and tooptimize cooling resources.

Most polymerization reactions today are run open loop with respect tothe product quality (end-use) properties. Also operations involved inthe manufacturing process are scheduled by a simple timer withoutattention to the actual progress of reaction.

In the last decade, the affordability of powerful computers finally madeit possible to exploit the advanced control concepts control theoristshave been developing since the 1960's. As a result, control ofcontinuous processes like refinery distillation columns or powergeneration units has seen a rapid evolution from single loopproportional, integral and differential (PID) controllers tomultivariable predictive controllers with built-in constraintoptimization whose performance cannot be matched by the old PIDsolutions.

For a number of reasons, this progress so far has avoided batchprocesses. Control wise, most batches are still run the way they werethirty or more years ago. If there was a change, it affected controlhardware, but not control algorithms. A batch recipe still prescribestime profiles of temperatures or pressures to be followed by a batchreactor in order to make the product. Feedback controllers, usuallyPID's, are routinely used to make the batch track the recipe in thepresence of variations in feedstock concentration and purity, catalystactivity, reactor fouling and so on.

Maintaining batch recipe temperatures and pressures is important but itshould not be the control objective. After all, the process owner doesnot sell batch temperatures or pressures. They are mere processparameters and, by themselves, are not even sufficient ones. It is wellknown and exemplified below for the case of polymerization processes,that two batches with perfectly identical temperature and pressureprofiles can still have different rates at which monomer is convertedinto polymer, and thus yield products with inconsistent quality. Whencomes to the end-use parameters of the real product, which aredetermining its marketable quality, most batch processes are still runopen loop, with all the negative consequences that an open loop recipeexecution entails.

With the present invention, that approach is replaced with a feedbackcontroller for polymerization processes that closes the loop using ameasurement directly tied to the product's marketable quality, and thusemploys feedback to eliminate quality variations and inconsistencies dueto the fluctuations of process inputs and operating conditions.

The invention is a polymerization control that allows the user tospecify independently the reaction mixture temperature and the degree ofmonomer conversion profiles as a function of time, and execute themunder feedback control. This both improves the run-to-run consistency ofthe product and reduces the uncertainty of the reaction time and coolantconsumption at any given instant. Because the coolant availability oftenis the limiting factor of production capacity, the improvedpredictability of individual batch runs offers an opportunity to improvebatch planning and scheduling and thus increase the plant yield withoutexpensive retrofits.

SUMMARY OF THE INVENTION

This invention enables the controller to employ feedback for the controlof product properties without the need for specialty sensors to measurethe properties and run the polymerization process on the basis of itsinner time reflecting its actual progress. As a result, the inventionmakes it possible, first, to manufacture polymers with consistentquality and, second, to improve process yield by allowing for betterutilization of the available cooling capacity without sacrificingprocess safety.

The invention includes an inferential sensor, whose concept is based onthe observation that for polymerization processes, in which heat isreleased by a single reaction, the amount of heat released isproportional, albeit in a nonlinear way, to the degree of the monomerconversion. Hence, by carefully calculating the reactor's thermalbalance on-line one can continuously infer the degree of conversion anduse it for control. Once the actual degree of conversion can bedetermined and ultimately controlled, one can also control the coolingduty of the reactor and thus make it conform with the cooling capacityallotted to it by the plant scheduler.

Superficially, an advanced batch control system utilizing theinferential sensor looks very much the same as a conventional one. Inboth cases, measurements of temperatures and flows of the reactorcoolant as it enters and leaves the reactor jacket or cooling coil willconstitute the bulk of input data. In addition to that data, theinferential sensor may require additional data reporting temperatures atsome other reactor spots and on the amounts and temperatures offeedstocks and catalysts. If some data on their composition areavailable, they can also be used with advantage for a more accurateinference.

The significant difference is in what the controllers do internally withthe data. In a conventional batch controller, the data are used directlyto control the reactor mixture temperature by manipulating the incomingcoolant flow and temperature. In an advanced controller, the data arefed into the inferential sensor instead, where they are used to inferthe current value of the degree of monomer conversion. This quantity isthen passed to the controller part of the advanced batch controller.

Even though the inferential sensor could be implemented as a stand-alonedevice and thus resemble physical sensors, this option is unlikely. Thereason is that the sensor involves a nonlinear dynamic model of both theprocess and the reactor, whose state must be kept in sync or coordinatedwith reality using a state estimation algorithm driven by the measuredtemperatures and flows. Once the model is available, it is shared withthe advantage of a model-based (nonlinear) controller.

Polymerization reactions are exothermic (i.e., a chemical change inwhich there is a liberation of heat, such as combustion). The overallamount of heat released by a reaction from its start up to a giveninstant depends on how much of the monomer(s) has been converted intopolymer. This measure of released heat indicating the degree of monomerconversion is a more reliable indicator of reaction progress thanphysical time because the same reaction can be running slower or fasterdepending on the initiator (i.e., catalyst) activity, reactant purityand other effects that may be difficult to measure directly. Moreover,for many polymerization reactions the degree of conversion is linked tothe product quality and thus can be used for closing the loop for theproduct quality feedback control in place of specialty sensors.

The degree of conversion is not measured directly, but the inventioninvolves inferring its running value by dynamically evaluating thereactor heat balance. This invention involves four concepts. First,there is the way of inferring the degree of conversion from the dynamicevaluation of the reactor heat balance. Second, the use of the degree ofconversion replaces specialty sensors for feedback control with respectto the product quality (end-use) properties. Third, the use of thedegree of conversion replaces physical time for the timing of processrelated operations like valve opening and closing, controlling the heatsupply/removal, dosing the reactants, and so forth. Fourth, the sensorallows an accurate prediction of the batch evolution and thus makes itpossible to accurately predict the cooling need profile from the currentinstant out to the batch termination.

In this invention, the reaction mixture temperature and the integralheat rate are treated as two independent process variables. Thisapproach provides the user the freedom to specify batch recipes in a waythat defines the evolutions of either variable during the batch run, andto execute them under tight, high performance control. Because thedegree of monomer conversion is proportional to the integral heat ratefor many important polymers including PVC, controlling the two variablesgives the user independent control over two basic determinants ofproduct quality. Even more importantly, such control fully defines theheat release at every instant of the batch run, thus making it possibleto better utilize the available cooling capacity through more reliableplanning and scheduling. To control the temperature and integral heatrate independently, the proposed method manipulates the amount of heatadded to or taken out of the reaction and the amounts of theinitiator(s) and inhibitor added during the batch run.

The present invention improves the yield of a PVC or polymerizationmanufacturing plant in two ways. First, this approach provides betterfeedback control of individual reactors, thus reducing the uncertaintiesof the reaction time and coolant consumption at any given instant.Because the benefit of plantwide planning and scheduling is dependent onthe quality of predictions that were used for the plan and scheduledevelopment, better reactor control is a technological enabler of betterplanning and scheduling. Specifically, more reliable predictions of thecoolant consumption allow the planner to run the plant with smallercooling capacity margins without sacrificing the plant safety, thusincreasing the plant yield. The controller of this invention canaccelerate or decelerate the reaction without changing the reactionmixture temperature. Consequently, it can reduce the reaction timewithout sacrificing the product quality by taking advantage of anyavailable cooling capacity. Second, this approach improves run-to-runproduct consistency and allows one to tighten the productspecifications, which also adds to the yield increase, by reducing theoff-specification production.

It is well known that some polymers could be produced by reactionsrunning at greater speeds without any significant degradation of theirquality, if only the reactors used could handle the increased heat flow.A good example is the manufacturing of PVC by the suspension process. APVC plant in Canada uses water from a river as a coolant for itsreactors. In the winter, when the water temperature is about 0.6 degreesCelsius (i.e., 33 degrees Fahrenheit), a batch takes about 5 hours tocomplete. However, in the summer, when the river water temperatureraises to 22 degrees C. (72 degrees F.), the same batch, with comparableproduct quality, takes 8 to 9 hours, because the drop in the availablecooling capacity forces the plant operator to slow down the reactionrate by using smaller amounts of the initiator.

In the above example, the coolant's supply is unlimited and therestriction comes from its increased temperature and limited watercirculation flow through the reactors' jackets. Another example is a PVCplant that uses chilled water as the coolant for its jacketed reactors.The plant has a centralized utility which supplies water to a dozen orso reactors. Because the chilled water is expensive and its supply islimited, water exiting the reactors is partly recycled by mixing it withthe freshly chilled water coming directly from the cooling towers. Thiscreates a variable production environment, wherein the availability ofthe chilled water depends on the number of batches currently in progressas some reactors are always being charged or discharged, while othersare temporarily out of service for cleaning and maintenance. Also, thechilled water temperature may fluctuate with the weather and the time ofthe day.

Before starting a batch, the operator must make a decision on how fasthe can afford to run it without risking a temperature runaway and choosethe appropriate amount of the initiator(s) which is then added to thereactor charge. To some degree, this decision is guesswork as theoperator has to consider the effects of gradual deposit buildup on thereactor walls on heat removal. Once the reaction gets going, theoperator can, in principle, speed it up or slow it down manually byadding the initiator or inhibitor, respectively, but this is notnormally done. Once started, the batch is run open loop without furtheroperator interference until its completion, which is indicated by thepressure drop in the reactor.

Given the uncertainty concerning the cooling capacity that will beactually available during the upcoming batch run and the impossibilityto exactly determine the initiator dosing beforehand and to correct itlater, the operator has to play it safe and make decisions that on theaverage might be overly conservative. This cuts into the reactor yield.Obviously, a better control over the actual rates of individual reactorsin the plant would make it possible to reduce the current technologicalmargins without endangering plant safety and thus create an opportunityto employ tighter plantwide optimization.

If one had better control over the reaction progress, then one couldeven think about more unusual ways to increase the plant yield.Currently, for each reaction the operator defines its speed before itbegins by dumping a particular amount of the initiator(s) into themixture. But there might be a window of opportunity when a large amountof chilled water is available, say, for two hours, because a couple ofother reactors happened to finish simultaneously and have to bedischarged and recharged. A batch controller that would allow theoperator to temporarily accelerate the running reactions for the twohours to take advantage of the unexpectedly available cooling capacityand then bring them back to the original rate by applying a suitableamount of an inhibitor, without disturbing the reaction mixturetemperature, would further improve the plant yield.

Making the batch follow a given temperature and conversion rate profilesnot only improves the quality and run-to-run consistency of its productbut, perhaps even more importantly, enables one to make accuratepredictions of the heat release during the batch run. As a result, onecan make reasonable and justifiable provisions for the expected coolingduty needed to keep the mixture at the desired temperature all the wayup to the reaction end, and thus better utilize available plantresources through more reliable plantwide planning and scheduling.

The present advanced batch control, along with the follow-up plantwideoptimization it enables, may have a major economic impact on plantperformance. Consider, for example, a plant with fifteen reactorsrunning so that the cooling capacity reserve is 10 percent. Since thecooling availability is the limiting factor, reducing the reserve tofour percent would increase its output by six percent, which is almosttantamount to adding another reactor to the plant, without the expenseof its construction and maintenance.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a diagram of a conventional polymerization reactor controllerfor batch control.

FIG. 2 is a diagram of the present polymerization reactor controller forbatch control.

FIG. 3 shows the inability, in principle, of existing approaches basedon controlling the reaction temperature T_(R) to reject processdisturbances affecting the conversion rate. This figure depicts apolymerization reaction by means of the thermokinetic equations, with anadded temperature control loop.

FIG. 4 shows an improved temperature feedback control for a batchpolymerization process, wherein the inferred information about theintegral reaction heat serves as a feedforward signal for bettertemperature control. A conventional, state-of-the-art reactiontemperature controller has no such feedforward.

FIG. 5 shows a simultaneous temperature and integral reaction heatfeedback control for a batch polymerization process.

FIG. 6 illustrates a way of estimating integral reaction heat flow fromremoved heat flow and mixture temperature. In reality, temperatures canbe simultaneously measured at more points to better reflect thedistributed nature of the chemical process.

FIG. 7 shows internal couplings of the process variables and theirdynamics as described by the thermokinetic equations.

DESCRIPTION OF THE EMBODIMENT

FIG. 1 shows a conventional batch controller 8. An advanced, highperformance controller 10 is shown in FIG. 2. Such controller needs moreinformation about the process being controlled. One needs to reconcilethe nonlinear nature of batches that calls for a one-of-a-kind,specialized controller for every polymerization process, with businessrequirements preferring a single controller easily customizable for aslarge a number of processes as possible. It is best to bring a gardenvariety of polymerization processes under a common umbrella.

It is unlikely that there will ever be specialty sensors for all kindsof end-use properties various polymers may have. If there is going to bea generic controller for batch polymerization processes, then it willhave to rely on inferential sensing of the properties instead of directmeasurement of them, and such an inferential sensor will have to be aninseparable part of the controller design. The sensor will infer itsreadings from the measurements of generic physical variables such astemperatures, pressures, flows, and so forth, that are easily obtainablefrom commodity sensors. Setting up the sensor will constitute a majorpart of the tuning of the controller for a particular application.

The present invention is applicable for a large class of polymerizationprocesses of practical importance. This approach is based on anobservation that for many processes, the degree of monomer conversioninto polymer is proportional to the overall amount of heat released bythe reaction since its start. Because the speed of conversion, plottedas a function of time, has a strong effect on molecular characteristicsof the resulting polymer chains and, therefore, the polymer end-useproperties, ensuring repeatable time profiles of the conversion speeds,are one of the keys to consistent product quality. One cannot easilymeasure the degree of conversion, but can develop algorithms whichpermit one to calculate estimates of the overall reaction heat, which inturn can be utilized as an inferred process variable for feedbackcontrol. Unlike the degree of conversion, measurement methods needed tomonitor the thermal conditions of a reaction are independent of aparticular polymer being produced, thus resulting in a preferred genericapproach.

First, there is a way for inferring the integral reaction heat of apolymerization reaction and its use for control. Initially, two uses ofthe inferred integral reaction heat are apparent. First, the integralreaction heat is used as another state variable of the process and usedto improve control of the reaction mixture temperature in the secondphase of a polymerization process, which is called the temperaturetracking mode of controller. (The first one is the startup mode, whichgives way to the temperature tracking mode when the controller switchesfrom heating the mixture to cooling it.) FIG. 3 shows a conventionalcontrol system 30 having a reaction mixture temperature feedback link52. For the sake of explanation, the process behavior is characterizedby the thermokinetic model, which reflects one's understanding of howthe process works. The sensor's applicability to polymerization processcontrol, as shown in FIG. 3, is useful for many polymers, but of limitedvalue for others. If the reaction mixture temperature T_(R) is to beheld constant throughout the batch process, as is the case, for example,in the PVC manufacturing; then the temperature control task is rathersimple. In other words, for the PVC case, after startup there is nodemanding temperature profile with steep up and down ramps for thecontrol system to track. It is no surprise, then, that conventionalcontrol systems can maintain the temperature within ±0.3 degree C. (0.5degree F.) and PVC manufacturing experts do not expect any productquality improvement from a more accurate temperature control.

FIG. 4 shows a system 40 having an improvement. This improvement is afeedforward link 53 to a controller 29, which informs the controllerabout anticipated changes of the integral heat rate caused by processdisturbances before they adversely affect the reaction mixturetemperature. That information is obtained from a process model 25 whichis a part of the inferential sensor. Second, the integral reaction heatserves as the "inner time" of the reaction, which better reflects itsactual progress than the ordinary, physical time and is used in thiscapacity to better time operations to be executed during the batch run.For example, the timing of stirring or mixing in additives is notderived from a clock, but from the integral reaction heat and is thusimplicitly or impliedly linked to the degree of monomer conversion.

FIG. 3 shows a feedback 52 execution of a batch recipe in the form of atemperature profile which cannot eliminate the impact of processdisturbances on the integral reaction heat, H(t) and, therefore, productquality. In reality, nothing on the process but the reaction mixturetemperature T_(R) is accessible for direct measurement. Of particularinterest are the degree of monomer conversion δ and the integralreaction heat rate H.

Block 12 of system 30 is a process model of the heat production in areactor. Input 13 indicates the amount of heat to be removed from thereaction in the reactor. Input 14 indicates the amount of heat producedby the reaction of the conversion of the monomer to a polymer, or heatrate of the reaction (which may be regarded as including disturbances31). Differential amplifier 15 outputs the difference of inputs 13 and14. This output is scaled by a scaling factor (1/cρ) 16. c and ρ maydepend on H. c and ρ are heat capacity and specific mass, respectively,of the reaction mixture. The scaled output is a rate of reactortemperature change dT_(R) /dt. This rate is processed by integrator 17resulting in an output T_(R) which is the reaction mixture temperature.T_(R) is input to a heat production rate determiner 18. Block 18 has anintegral reaction function h which is applied to reactor temperatureT_(R) and integral reaction heat H. Also inputs are actual processdisturbances 31 of the reactor which may include the effects of aninhibitor or initiator, the condition of the reactor, and other factors.The output of block 18 is a rate of heat dH/dt production of thereactor. That output is integrated by integrator 19 to provide theintegral reaction heat H. That output H is fed back into block 18 to beprocessed as a function of h. Also, H goes to a function block 20 thatconverts or calculates the amount of heat determined into the degree ofconversion of the monomer into a polymer in the reactor, at output 21.

System 30 controls the reaction in accordance with desired temperatureT_(R) desired which is fed along with the actual or calculated integralreaction temperature into a summer 22. The output of summer 22 is thedifference of the actual and desired reactor temperatures which goes tocontroller 23 which determines the amount of heat that should be removedwhich is to effectively control the cooling water or the temperature ofthe reaction. Block 24 covers the feedback temperature control of thepolymerization process of system 30.

FIG. 4 reveals system 40 which shows how control of the reaction mixturetemperature T_(R) is improved by informing controller 29 aboutanticipated changes of the integral heat rate H. Here feedbacktemperature control is affected by a feedforward signal 53 which is anintegral reaction heat H indication from integrator 19 of reactionprocess model 25. Only the reaction temperature T_(R) is accessible formeasurement. In order to estimate H, inferential sensor system 40involves reaction model 25 process which is maintained in sync with theactual polymerization process in block 26. Reaction model 25 process isnot subject to disturbances and nor is the model reaction processtemperature T_(R) utilized as a feedback signal for affecting reactionmodel 25 process. However, like block 12 of FIG. 3, polymerizationprocess 26 is affected by reaction temperature T_(R). Feedforward signal53 indicating the amount of reaction heat of model 25 goes to controller29. Also to controller 29 is a difference 48 between the desiredreaction temperature 47 and the actual reaction temperature 52 fromsummer 22. In the present invention of FIG. 5, system 50 has a feedbackcontrol of reaction temperature T_(R) 52 and integral reaction heat H 53(i.e., which indicates a degree of conversion). This involves amodification of the reaction simulation, that is, polymerization process26 and reaction process model 25, so that they allow for the on-linedosing 32 of initiators (and possibly of an inhibitor as well if theuser wants or needs it) as another manipulated variable in addition tothe coolant flow to the reactor. This gives the extra degree of freedomneeded to control simultaneously and independently both the reactionmixture temperature and the rate of conversion, which are independent,though coupled state variables of the polymerization process. Thedesired reaction temperature T_(R) desired 47 is input to summer 22 andcombined with the reaction temperature T_(R) 52 fed back from the outputof polymerization process block 26. The output of summer 22 is adifference 48 between the desired reaction temperature 47 and actualreaction temperature T_(R) 52 and it goes to controller 35. The desiredintegral reaction heat production H_(desired) 54 and the actual integralreaction heat production H 53 from the output of integrator 19 asindicated by the inferential sensing of reaction model 25 process, areinput to summer 36 which outputs a difference 55 of the desired 54 andinferred actual 53 integral reaction heat productions H. This difference55 is input to controller 35. Multivariable predictive batch controller35 controls the two variables to their respective set point profiles ina decoupled fashion using the inferential sensor 56 like that of system40 in FIG. 4, to infer the rate of heat production dH/dt 14. The twooutputs T_(c) 58 and f_(c) 61 of controller 35 manipulate the amount ofheat, q_(tot), via line 13, taken out of the reaction by the reactor'scooling/heating system, and the amount of the initiator/inhibitor, D,via line 32, added into the reactor. Controller 35 accounts fordifferent activities of various initiators or inhibitors that may beused. Reaction model 25 process is a part of inferential sensor 56 ofsystem 50.

One should note that the above is a simplified description of controller35. Its actual implementation involves more but less significantvariables. For example, q_(tot) comprises all heat removal-relatedvariables of the process that allow for manipulation, including waterflow through the cooling jacket 59 and coils, and cooling watertemperature at inlet 38 and outlet 40, and so forth of the reactor 60(FIG. 6).

Minimum reactor 60 instrumentation is needed. One turns thethermokinetic equations of a polymerization reaction process 26 into aform of model 25 that is suitable for real time control. Both the formand reactor model 49 involve parameters that need to be estimated on theactual process 26, some of them off-line, some on-line. In order to doso, one collects data on certain process variables. The minimum set ofthe measured variables is schematically shown in FIG. 6. They are: T_(R)--reaction mixture temperature from temperature sensor 27 in reactor 60;p--reaction mixture pressure from pressure sensor 28 in reactor 60;T_(CI) --input cooling water temperature from temperature sensor 37 inwater input pipe 38 to reactor 60; T_(CO) --output cooling watertemperature 58 from temperature sensor 39 in water output pipe 40 fromreactor 60; f_(C) --cooling water flow rate 61 from flow sensor 41 inpipe 38; P_(a) --agitation power required to rotate agitator or mixingblade 42 in mixture 43 in reactor 60 at a rate of n revolutions perminute, from sensor 44. Valve 45 provides for the entry of cooling waterand the exit of the water from jacket 59 of reactor 60. Pump 46 ensuresthe flow of the cooling water to and from reactor 60 jacket 59. Thesemeasured variables are input to reactor model 49. Induction periodlength T_(I) is input to reactor model 49. T_(I) is the period of timeor delay before the polymerization reaction starts after the initiatoris added to the batch mixture. An indication of the amount of heatremoved from the reaction, q_(tot), is input to block 25 which processesthe thermokinetic equations. Also input to block 25 is T_(R0) which isthe initial reaction temperature. H, the indicated integral reactionheat 53, is output from block 25. The degree of monomer conversion δ 21of the batch mixture is inferred from integral reaction heat H 53.

For the reactor model 49 development, it is recommended that one havethe reactor blueprint (or at least a sketch of its physical arrangementand dimensions) as well as the placement and quality of the sensors.

The heat that polymerization reactions produce must be removed from abatch reactor by its cooling system. If a reaction is not to end up in atemperature runaway, its heat production rate must be matched by therate at which the cooling system removes the heat from a reactor.Because the heat production rate is proportional to the rate at whichmonomer is converted into polymer, it is the cooling system capacitythat ultimately limits the yield of the reactor. The optimal utilizationof the available cooling capacity of a plant thus becomes a determinantof its product yield.

The direct benefit of using the controller over existing solutions is toget a batch under feedback control both with respect to its reactionspeed and mixture temperature and thus tighten the manufacturingspecifications which are being constantly threatened by unpredictablevariations in the initiator activity and feed impurities. The recipes tobe used with the proposed controller are more accurate, because inaddition to the temperature profile they also specify the desired degreeof monomer conversion profile over the batch run. Since for a class ofpolymers specified in the approach in FIG. 4 the degree of monomerconversion δ is proportional to the integral reaction heat H, the batchrecipes can be defined directly in terms of H 53, and not of δ, as afunction of time, in view of the approach in FIG. 5. This simplifies thecontroller setup because there is no need to develop the nonlineartransformation block f(H) 20 shown in FIG. 3.

Below are stated the thermokinetic equations (4) and (5), modeled byblock 25, of a polymerization reaction. Polymerization reactions areexothermic. The amount of heat being released at any given time,however, is not constant throughout the reaction but varies in time as afunction of the reaction mixture temperature and the degrees ofconversion of individual monomers involved in the reaction. Let onedenote the amount of heat produced by one cubic meter of the reactionmixture per second as

    h(T.sub.R (t), δ.sub.1 (t) . . . , δ.sub.N (t))(1)

where δ₁ (t), . . . , δ_(N) (t) are degrees of conversion of variousmonomers at the time t, and T_(R) (t) is the mixture temperature, andcall it the heat production rate. Its dimension is [J/m³.s].

The overall amount of heat, H(t), produced since the reaction wasstarted at t=0 is obtained by integrating the differential equation##EQU1## and is called the integral reaction heat. Its dimension is[J/m³ ].

There is a large class of practically important polymerizationreactions, which involve either only one monomer or multiple monomersreacting at the same kinetic rates. Or, to define the class in the mostgeneral terms, one can say that its members are distinguished by havinga single heat producing reaction, which may be chaining up one or moremonomers (as is the case, for example, in the production of nylon). Forsuch reactions, their single degree of conversion, δ(t), is in aone-to-one relationship,

    δ(t)=f(H(t))                                         (3)

with the integral reaction heat, H(t), and the equation (2) can bewritten as follows: ##EQU2## The function h(T_(R) (t),H(t)) is calledthe heat rate and is specific to a particular process. The releasedheat, H(t), along with the heat removed from the reaction mixture 43,q_(tot) (t), defines the mixture temperature, T_(R) (t): ##EQU3## Herec(t) and ρ(t) are the heat capacity and specific mass of the mixture,respectively. Both of them generally change with time as the reactionprogresses. Their dimensions are [J/kg.°K] and [kg/m³ ], respectively.

q_(tot) (t) is the removed heat flow, that is, the total amount of heatremoved from 1 m³ of mixture 43 per second from external sources by allmeans, i.e., through cooling, heat losses, and so forth. If heat isadded, for example through agitation by blade 42, q_(tot) (t) mightbecome negative. Its dimension is [J/m³.s].

The equations (4), (5) are referred to as the thermokinetic equations ofa given polymerization reaction. FIG. 7, in the box named "reactionmodel" 25 shows a schematic of the application of these equations andtheir dynamics. It shows their internal structure and mutual couplingsof the process variables. Also shown in FIG. 7 are the equationscharacterizing the heat removal from reactor 60, which are explainedbelow.

For the thermokinetic equations to be valid in the above form, reactionmixture 43 must be perfectly mixed so that its temperature, T_(R) (t),is uniform throughout the batch reactor volume. For some processes thisassumption may be difficult to uphold, particularly toward the end ofreaction, when the mixture might gel or even glassify. In such cases,the lumped parameter model of equations (4), (5) must be replaced by adistributed one. For PVC made using the suspension process, a huge watervolume present in reactor 60 keeps the mixture viscosity low and makesgood mixing possible, thus justifying the use of the lumped model. Italso largely suppresses the effects of progressing polymerization on thespecific heat and weight (i.e., specific mass) of mixture 43. Therefore,one assumes c(t) and ρ(t) to be constant throughout the batch.Furthermore, to simplify the notation, one can drop the time t fromcertain symbols in the equations and figures.

Similar assumptions are applicable for many other polymerizationprocesses as well. If some of them are not, then it is possible tomodify the mathematical form of the exothermic equations to satisfy thetechnicalities, while retaining the idea of using them.

In order for the thermokinetic equations to be applicable forinferential sensing and control, one has to determine the heat rateh(T_(R) (t),H(t)) and the total amount of heat q_(tot) removed from theprocess. Let one postpone the former until later and outline now how toobtain the latter.

Heat is usually removed in several ways simultaneously, the major onebeing through the cooling system. Others are heat losses to the ambientdue to lack of reactor insulation, heat escaping in gases intentionallyreleased to maintain reactor pressure, heat absorbed by added reactantsto bring them to the mixture temperature, etc. There might also be heatflow entering the reaction, however, most notably through the energyneeded to agitate mixture 43. Let one consider the total heat to be asum of three major components,

    q.sub.tot =q.sub.C +q.sub.A +q.sub.M,

where

q_(C) is heat 62 removed through the reactor's cooling system,

q_(A) is heat 63 escaping into the ambient through the reactorinsulation (if there is any at all), and

q_(M) is a "catch-all" term introduced to account for miscellaneousother heat escape routes, termed as miscellaneous heat 64. Depending onparticular process, some of them may be significant enough to deserve tobe explicitly modeled. The sum of q_(C), q_(A) and q_(M) is achieved bysumming amplifier 68 as an ouput q_(tot) signal 13 to amplifier 15 ofreaction model 25. Heat flux 62 crossing the reactor wall from themixture into the cooling medium is ##EQU4## where R_(C) (H,f_(c)) is theheat transfer coefficient 65 from mixture 43 into the coolant, whichgenerally depends on the mixture viscosity which, in turn, is related tothe degree of conversion and thus to the integral heat H as well, andalso on the coolant flow f_(c) 61,

T_(R) is the reaction mixture temperature 52,

T_(C) is the coolant temperature 58,

a_(C) is the area of the wall across which the transfer happens, and

V is the mixture 43 volume.

Although the above expression is correct, it cannot be used in thissimple way to actually calculate q_(C) because the coolant temperatureT_(C) in the jacket is not uniform. Nevertheless, in conjunction withthe thermokinetic equations it conceptually explains the controller 35affects the polymerization by adjusting the coolant temperature 58.Because the actual coolant temperature raises as the coolant flowsthrough the jacket, the average temperature can also be decreased byincreasing the coolant flow f_(c) 61 and vice versa.

A similar formula holds for the heat flux 63 escaping into the ambient:##EQU5##

R_(A) (H,f_(c)) is the heat transfer function coefficient 66 frommixture 43 into the ambient. Of course, there is no way one canmanipulate the ambient temperature T_(A), but its measurement is used asa feedforward signal 67 to better estimate this heat loss 63. For highlyviscous mixtures 43, power 44 needed to agitate them may be large enoughto demand its explicit inclusion as a heat contributor.

Reaction model 25 process is synchronized with actual polymerizationprocess 26 by model state coordinator 69. Synchronization orcoordination is cued from a comparison signal 70 from differentialsummer 72 having as inputs reaction temperatures T_(R) 52 frompolymerization process 26 and reaction model 25, by coordinator 69 whichoutputs a synchronizing or coordination signal 71 to amplifier 15 ofreaction model 25 to maintain the state of model 25 to be the same asthat of process 26.

Coolant temperature T_(C) signal 58 and reaction temperature T_(R)signal 52 are summed by amplifier 73. The output of amplifier 73 ismultiplied by coefficient a/V 74 where a is the surface area of reactor60 where heat exchange is taking place. The output from coeficient block74, along with f_(c), signal 61 and H signal 53 goes to heat transfercoefficient block 65 which outputs a q_(c) signal 62.

Ambient temperature T_(A) signal 67 and reaction temperature T_(R)signal 53 are summed by amplifier 75. The output of amplifier 75 ismultiplied by coefficient a/V 76 where a is the surface area of reactor60 where heat exchange is taking place. The output from coeficient block76, along with f_(c) signal 61 and H signal 53, goes to heat transfercoefficient block 66 which outputs a q_(A) signal 63. Amplifier 68receives q_(c) signal 62, q_(A) signal 63 and miscellaneous heat q_(M)signal 64 and sums them into an ouput q_(tot) signal 13 fed to amplifier15.

Conventional batch controls cannot guarantee product consistency. Assumethat a recipe specifies a desired batch temperature profile,T_(Rdesired) (t), 47, and a conventional temperature control systemensures that this profile is perfectly followed by actual reactortemperature T_(R) 52, i.e.,

    T.sub.R (t)=T.sub.Rdesired (t)

Now consider two batches in which different amounts of the initiator(catalyst), as prescribed by signal 32, were used. Different initiatorconcentration causes the two reactions run at different speeds and,consequently, their heat production rates as well as their integralheats will differ:

    h.sup.(1) (T.sub.R,H.sup.(1))≠h.sup.(2) (T.sub.R,H.sup.(2))

Their temperature profiles T_(R) (t), however, can still be maintainedperfectly identical by the temperature control system, which properlymanipulates the amounts of heat, q.sup.(1)_(tot) and q.sup.(2)_(tot),taken out of the mixture by the reactor cooling so that the equations(5) corresponding to each batch hold despite variations in H.sup.(1)(t), H.sup.(2) (t): ##EQU6##

Obviously, unless the control system keeps track of how much heat wasadded to or removed from the mixture as a result of its control actions,then one may not even find out that the two seemingly identical batchesactually ran at different conversion speeds.

The present contention is that feedback batch temperature control stillruns the batch open loop with respect to the integral heat rate 14,H(t), and also as to the degree of conversion 21, δ(t), as revealed inFIG. 3. Process disturbances 31 affecting the heat rate, h(T_(R),H),which, in turn, also affect the mixture temperature 52, are seen bycontroller 23 as external disturbances 31 and their thermal effects arerejected, while they are free to let H(t) 53 and, consequently, δ 21fluctuate without any correction. Feedback execution of a batch recipein the form of a temperature profile cannot eliminate the impact ofprocess disturbances on H(t) and, therefore, product quality.

A concept of advanced polymerization control has a main idea which is toclose the loop using integral reaction heat 53, H(t), output ofintegrator 19, as a substitute for the desired degree of conversion,δ(t), which would be extremely difficult to measure directly and wouldrequire specialty sensors for different polymers. The integral reactionheat H(t) is directly related to product quality. Unless processdisturbances 31 are entering the nonlinear mapping f(H) 20, thissimplification permits skipping modeling without degrading the controlperformance. For instance, reaction mixture 43 agitation so vigorousthat it impacts the distribution of polymer chains lengths might be anexample of such a disturbance. In contrast, FIG. 3 shows temperatureT_(R) feedback 52 rather than the heat H feedback 53.

Usual process disturbances, be they fluctuations of the initiatoractivity or monomer concentration, effects of impurities and others allshow up as changes of the heat rate h(T_(R),H). Because the heatcapacity and weight of the mixture are either known or can be easilydetermined, h(T_(R),H) is the only missing piece of knowledge. Thisfunction of two variables represents a mathematical encoding of chemicalfacts about the given reaction and therefore will be different fordifferent processes. Some of the facts represent the knowledge that canbe extracted beforehand (i.e., off-line) from books or historical datacollected on the process. Some other facts, such as initiator activity,depend on so many unmeasurable contributions that the only way to findout is to either measure or estimate it on-line from data collectedwhile the batch to be controlled is already in progress.

To estimate with a reasonable accuracy a function of two variables withno prior information about a process functional form is a formidabletask whose completion would require large amounts of data, more than canever be collected from a single batch run. On the other hand, because amodel is needed for controlling the very batch on which data is beingcollected, one has to develop h(T_(R),H) very early into the batch,while it still is in its initial phase, without the luxury of havingdata from a complete run. This presents a dilemma. On one hand, oneknows that h(T_(R),H) will always contain something that is specific foreach batch run and thus implying that h(T_(R),H) be estimated anew inevery run. On the other hand, it is clear that data collected at thebeginning of a single run would never suffice to compute a goodfunctional estimate.

The answer to resolving this dilemma lies in factoring h(T_(R),H) intotwo components. One component will contain only knowledge that ispermanent, independent of a particular run. This component can beestablished beforehand, using both chemical theories and historicaldata. Because its computation is done off-line, one is free to use asmuch data as one pleases and employ sophisticated, but time-consumingalgorithms to do the job. The other component will contain onlyknowledge which is valid only in a particular run and thus needs to beextracted on-line. Because the amount of available run time data issmall, the amount of this knowledge must be kept to an absolute minimum.One can safely say that the ability to do the h(T_(R),H) factorizationcorrectly is the key to success of the proposed approach. This is theplace where expertise in polymer chemistry is necessary in order to comeup with factorizations that stand a chance both to reflect the chemicalreality and to be fitted using limited amounts of data.

The heat production rate h(T_(R),H) is factored. For the sake ofexplanation, let one think of the estimation of h(T_(R),H) as a two stepproblem. The first step is to estimate the integral reaction heat flow,dH(t)/dt, knowing the removed heat flow, q(t), and the mixturetemperature, T_(R) (t). The specific heat, c, and weight, ρ, of themixture are assumed to be known.

This is a trivial problem once one knows q(t). Because heat is anintegral quality, it cannot be directly observed and must be computedfrom temperature and flow measurements. The computation of q(t) for agiven reactor is the real challenge in this step. This computation isdiscussed below.

The second step is to estimate h(T_(R),H), knowing the integral reactionheat flow, dH(t)/dt, from the first step and the mixture temperature,T_(R) (t).

The formidable task of function estimation mentioned above, which, inthe present application, cannot be solved without a suitablefactorization. Here one proposes to factorize h(T_(R),H) as a product oftwo functions of a single variable, s_(T) (T_(R)) and h_(H) (H), and ascaling constant s₀,

    h(T.sub.R,H)=s.sub.0 ·s.sub.T (T.sub.R)·h.sub.H (H)(6)

and proposes s_(T) (T_(R)) to be of this particular form ##EQU7## whichcan be justified by assuming the reaction rate to accelerate withreaction temperature according to Arrhenius. Here

E is the activation energy of the polymerization reaction,

R_(G) is the universal gas constant,

T_(R) (t) is the actual temperature profile of the reaction mixture,

T₀ is the constant reference temperature,

h_(H) (H) is the nominal heat production rate observed at the referencetemperature,

s_(T) (T_(R)) is the temperature factor due to temperature differences,

s₀ is a "catch-all" scaling factor called the reactivity to account forother variations.

The value of equations (6) and (7) is in allowing one to transform datacollected during batches, whose temperature profiles differ from thenominal one, as if they were collected under the nominal conditions.Once one knows how to remove the effects of temperature variations, datafrom many batches to estimate the nominal heat production rate, h_(H)(H), can be used. However, before one can remove such effects, knowledgeof how to eliminate the effects of initiator activity is needed.

First, accounting of the effects of initiator activity is needed. Manypolymerization reactions will not run at all or only at very lowconversion speeds unless an initiator (catalyst) is used. Because theinitiator activity defines the reaction speed, its effects must besomehow encoded in h_(H) (H). But the initiator activity is a veryvolatile aspect which may change from run to run and cause largefluctuations in the batch behavior. Unless one explicitly removes theinitiator activity effects out of the historical data and thus, ineffect, renormalize the data to a "standard initiator activity profile",the resulting estimate of h_(H) (H) might easily be a flat average whichis not particularly good for any actual batch. Also, if the estimate ofh_(H) (H) is to be of any use for control, one must know how tocustomize it for every future batch using its actual initiator activityprofile.

Before incorporating the initiator effects into h_(H) (H), a few factsabout what happens to the initiator in the course of a polymerizationreaction need to be known. Although polymerization reactions do notconsume the initiator, its concentration nevertheless keeps falling inthe course of a reaction mainly due to two effects. As to the firsteffect, immediately after adding the initiator to the mixture, thepolymerization reaction does not take off immediately. It appears thatthe initiator's activity is temporarily hindered by impurities presentin the input stocks. Among chemical engineers, this delay (denote itT_(I)) is known as the induction period. Because the amount ofimpurities in a batch is virtually impossible to determine beforehand,both the induction period and the actual initiator concentration at thetrue beginning of the batch reaction are unknowns that must be estimatedon-line.

As to the second effect, many initiators are high energy compounds andas such tend to be chemically unstable. During a batch run, theinitiator typically undergoes a spontaneous disintegration whichexponentially (or even faster) lowers its concentration in the mixture.Also, long storage of the initiator compound tends to degrade it andunless the initiator activity is measured before its use, thedegradation will introduce an unmeasured disturbance into the batchprocess.

To account for those phenomena, one assumes the following three points.First, the nominal heat production rate is proportional to the initiatorconcentration, [I]:

    h.sub.H (H)=[I]·h.sub.I (H)                       (8)

where h_(I) (H) is also called the nominal heat production rate but thistime normalized with respect to both the reaction temperature and theinitiator concentration.

Second, the polymerization reaction starts only after the inductionperiod. From the modeling point of view, the period is a pure delay.

The initiator's spontaneous disintegration proceeds as the first orderreaction ##EQU8##

If the initiator is added in the course of a reaction, the equationneeds be amended by an appropriate driving force term.

As factorization (8) implies, in order to develop the estimate h_(H)(H), one has to know both the solution, [I] (t), of equation (9) and theestimate h_(I) (H). Whereas the latter is always estimated off-line andthus one's choice of a suitable computational method is constrainedneither by data availability nor real-time concerns; this is not truefor [I] (t). As discussed above, the initiator concentration can varyfrom batch to batch and thus must be estimated on-line from scarce realtime data collected early into the batch run. This severely limits thepresent options as to how to proceed.

Equation (9) is linear but with a time-varying coefficient, because thekinetic rate, k_(I) (T_(R) (t)), depends on the reaction temperatureT_(R) (t). Its solution ##EQU9## shows that disintegration isexponential in time and generally accelerates with growing temperature.To fully determine the solution, one has to estimate the initialconcentration [I](T_(I)) at the end of the induction period (i.e., atthe beginning of the polymerization reaction), the induction periodlength T_(I) and the variable kinetic rate k_(I) (T_(R)). The first twoare scalar numerical values, which are easy to estimate, the third oneis a function of a single variable T_(R).

If nothing is known about a function being estimated, then one has toconstruct its estimate by a nonparametric estimation method. However, toproduce reliable results such methods generally require so much datathat one can rule them out in these circumstances. The only sensibleapproach seems to be to replace the nonparametric function estimation bya parametric one by inserting a piece of chemistry knowledge regardingthe likely form of the function k_(I) (T_(R)). Because any estimationbased on a limited amount of data is always a tricky business, everypiece of knowledge one can get about the resulting function up frontwithout having to estimate it goes a long way in stretching the value ofthe available data because it greatly reduces the amount of knowledgethat needs to be correctly extracted. Below is a possibility for whichone can put forth some chemical justification:

Assume the disintegration kinetics to be of the Arrhenius type. Then,one can express k_(I) as ##EQU10## where k_(I0) is the kinetic rateconstant at the nominal temperature T₀, and

E_(I) is the activation energy.

Since E_(I) can be assumed to be known, the original problem ofestimating the function k_(I) (T_(R)) boils down to the estimation ofthe single numerical constant k_(I0).

The initiator concentration drops over time since the moment theinitiator was added into the reaction mixture at the time 0. Althoughthe concentration [I] (0) at this moment can perhaps be calculated fromthe input stock amounts and then projected into the future value[I](T_(I)) using the equation (10), the actual amount of the initiatorat the time T_(I) can be a way off from such projection due to otherunmodeled effects taking place during the induction period. Theseeffects can be brought into consideration by expressing the actual value[I](T_(I)) as a function of the value [I] (0) as follows: ##EQU11##

The scaling constant s represents an uncertainty due to the unmodeledeffects and as another multiplicative constant might be eventuallyincluded in the reactivity s₀ introduced earlier in (6).

The nominal specific reaction heat h_(I) (H) can be estimated. Finally,one is in a position to devise a complete approach to estimate thenominal heat production rate h_(H) (H). Recall that one began byexplicitly introducing the effects of the initiator concentration [I] inthe form

    h.sub.H (H)=[I]·h.sub.I (H)

followed by assumptions concerning the initiator disintegration and thedelayed onset of the polymerization reaction, ##EQU12## in which onemade yet another assumption to convert the estimation from functional toparametric to make the problem solvable using small data sets: ##EQU13##

The proposed factorization of the heat production rate outlined aboveshould be thought of as a working hypothesis that may need amendments toaccount for specifics of any particular polymerization process. Henceits validation is the first step to take when applying the approach to anew process.

Now one will consider two estimation problems whose objective is toobtain the factors from experimental data. In both, the function h_(H)(H) is known from the first step (see the discussion above on factoringthe heat production rate), at least for H(t) for t ranging from t=0 upto the current time t or, in the case of archived data, till the end ofthe batch run, T_(B). Also, one assumes that the temperature profilesT_(R) (t) and T₀ (t) are available, and the activation constant E_(I) isknown. (If not, then it can be either established independently orestimated like any other parameter.)

The first problem is estimating h_(I) (H) from archived data. This is anoff-line procedure. From a set of N batch records, one first extractsthe nominal heat production rates h_(H) (H).sup.(n), n=1, . . . , N.Although the rates all are outcomes of what should be the samepolymerization reaction, they will generally differ as a result ofdifferent initiator concentration drop rates and other disturbances.Whereas the same desired heat h_(I) (H) must be universally valid forall batch runs, the constants T_(I).sup.(n), [I₀ ].sup.(n),k_(I0).sup.(n) are not. One highlights the fact by marking them with thesuperscript denoting their batch number. Even though the constants areof no use, one has to estimate them for each batch in order to get h_(I)(H) right and then one simply tosses them.

A possible formulation of the problem is as follows. Let the h_(I) (H)estimate be expressed in the finite series form ##EQU14## where Φ_(m)(H), m=1, . . . , M is a suitable set of basis functions and w₀, . . . ,w_(M) are unknown weights.

Because the shape of h_(I) (H) is basically given by the order of thereaction kinetics, the basis set needs to be defined so that its membersreflect the reaction order as well as effects not covered by kinetics(e.g., gelation).

Find

    W.sub.0, . . . , W.sub.M, T.sub.I.sup.(1),[I.sub.0 ].sup.(1),k.sub.I0.sup.(1), . . . , T.sub.I.sup.(N), [I.sub.0 ].sup.(N),k.sub.I0.sup.(N)

such that they minimize the fitness criterion ##EQU15##

Aside from its apparent complexity, this is conceptually a plainnonlinear problem.

The second problem is estimating T_(I),[I₀ ],k_(I0) from real time data.This is an on-line procedure used during real time batch control. Itsobjective is to find the likely values of T_(I),[I₀ ],k_(I0), whichcharacterize the initiator activity in the current batch. Now the heath_(I) (H) is already known. A possible mathematical formulation of theproblem is to find T_(I),[I₀ ],k_(I0) such that they minimize thefitness criterion is ##EQU16##

Notice that now the integral runs only up to the current time t.Ideally, the minimum will be recomputed over and over as the batchprogresses thus allowing for continuous updates of the initiatoractivity model. Another approach can incorporate the nonlinear extendedKalman filter theory.

One may develop algorithms to solve the above problems. The removed heatflow q is calculated in the first step on factoring the heat productionrate. Once one knows it, the estimation of the heat flow dH/dt issimple. Now one can focus attention on how to calculate qt.

There are several items to note. First, heat is an integral property andthus has to be calculated from instantaneous measurements like those oftemperatures, pressures, flows and so forth. Second, heat generated bythe polymerization reaction can be stored in the reactor in a number ofways. In other words, the heat that one is measuring as exiting thesystem through the cooling medium or thermal losses may be only afraction of the heat that is actually being generated at any given time.To produce a realistic picture of all heat flows requires a meticulousanalysis of the production equipment, especially for continuousprocesses. Third, when it comes to heat transfer, reactors are notuniform. Some parts of reactor walls or coolers do a better job thanothers and, as a result, one might be forced to describe the reactors byfinite element models, even though the simpler, lumped parameter modelsare sufficient for a number of processes. The models involve heattransfer coefficients that must be experimentally determined to makesure that they agree with the physical reality.

The reactor provides an environment in which the polymerization reactionis executed. It interfaces with the reaction through heat transfer, thuschanging the reaction mixture temperature T_(R) and, consequently, thespeed of monomer conversion. However, the interaction works in the otherdirection as well. Because the heat transfer coefficient at the boundarylayer between the mixture and reactor walls, R_(RW) (H), depends on themixture viscosity, the amount of heat removed from the reaction willdepend on the current degree of conversion and thus on the integralreaction heat H, all other things being equal. On the outer side of thewall, the heat is removed by the coolant flowing through the reactorjacket or cooling coils. Because the heat transfer coefficient betweenthe wall and the coolant, R_(WC) (f_(C)), changes with the coolant flow,f_(C), which generally is not constant, one must also know therelationship R_(WC) (f_(C)) for a range of flow values.

The heat transfer coefficient R_(WC) (f_(C)) (or, rather, heat transfercoefficient function) is not related to a particular polymerizationprocess. Similarly, if the mixture-to-wall coefficient is expressed as afunction of viscosity, R_(RW) (viscosity), instead of the integralreaction heat, R_(RW) (H), then it would be largely independent of theprocess, too. It may happen that both coefficients have already beenestablished in process-independent forms by the reactor manufacturer andare provided in the reactor documentation, or they have been measuredearlier as a part of some other project. If this is not the case, thenthe coefficients must be determined experimentally. Of course, if R_(RW)(viscosity) is available, then one still has to determine experimentallythe relation between the integral reaction heat and viscosity for thegiven process:

    viscosity=v(H)                                             (17)

Sometimes the reactor is cleaned up periodically but not after everybatch and a gradual buildup of deposits on the reactor walls may occur.The deposit layer impacts the coefficient R_(RW) (H) which then requireson-line corrections.

When the reaction is in progress, an algorithm involving the conceptsdescribed above, but extended to handle both the thermokinetic andreactor model equations as well as the state update in addition to themere parameter estimation, will keep the models in agreement with thereal process. Because of their continuous update, the models are farmore accurate than any off-line model established once the system iscommissioned. Such models not only improve the performance ofmodel-based process controllers, but have applications beyond theclassic control theory field. In particular, the controller can sharemodels with the production planning and scheduling packages. Thisvertical integration is perhaps the most economically attractive featureof this invention.

In the PVC manufacturing (and possibly other kinds of manufacturing), acomparable product quality can be achieved at different conversion ratesas long as the mixture temperature is kept constant. This makes itpossible to accelerate or decelerate the reaction, with the onlyrestriction being the ability to remove the released heat. The coolingcapacity, though, is always limited. In principle, the scheduler eitherknows or can decide how much cooling capacity can be allocated to eachreactor at any particular time a few hours ahead. An optimizer then cancustom-design the integral heat (or degree of conversion) recipe for thereactor so that while tracking it, the controller will make its coolingduty output match the allocated cooling capacity and dose theinitiator/inhibitor so as to maintain the mixture temperature constant.This will guarantee the fastest reaction for the desired temperature,and thus will maximize the reactor throughput. At the same time, bettermodels will make planning and optimization more reliable, thus reducingthe need for large safety margins without endangering the plant safety.

We claim:
 1. A batch polymerization process control device forcontrolling a batch process in a reactor, comprising:a controllerconnected to the reactor, for receiving a process temperature feedbacksignal from said reactor and providing reactor cooling control signalsto said reactor; and an inferential sensor, connected to said reactorand to said controller, for receiving parameter signals from saidreactor, providing a reaction model heat feedforward signal to saidcontroller, and receiving reactor cooling control signals from saidcontroller.
 2. The batch polymerization process control device of claim1, wherein said controller comprises a summer for receiving the processtemperature feedback signal and a predetermined process temperaturesignal, and outputting a signal indicating a difference between theprocess temperature and the predetermined process temperature.
 3. Thebatch polymerization process control device of claim 2, wherein saidinferential sensor comprises:a reactor model wherein said reactor modelreceives parameter signals from said reactor and the reactor coolingcontrol signals from said controller and outputs a signal indicatingtotal heat removed from said reactor; and a reaction model for receivingthe signal indicating the total heat removed from said reactor andproviding the reaction model heat feedforward signal to said controllerand to said reactor model.
 4. The batch polarization process controldevice of claim 3, inferential sensor further comprising a coordinatorfor receiving a reaction model temperature signal from said reactionmodel and the process temperature feedback signal from said reactor,coordinating corresponding states of activity and simulated activity ofsaid reactor and said reactor model, respectively, and outputting acoordinating signal.
 5. The batch polarization process control device ofclaim 4, wherein said reaction model comprises:a combiner for receivingthe signal indicating the total heat removed from said reactor and thecoordinating signal, and having an output; a scale factor adjusterhaving an input connected to the output of said combiner, and having anoutput; a first integrator having an input connected to the output ofsaid scale factor adjuster, and having an output that provides thereaction model temperature signal to said reactor model and to saidcoordinator; a first processor having an input connected to the outputof said first integrator, having an output for providing a rate ofreaction model heat production signal to said combiner; and a secondintegrator having an input connected to the output of said firstprocessor and having an output for providing the reaction model heatfeedforward signal to said controller, to said reactor model, and to theinput of said first processor.
 6. The batch polymerization processcontrol device of claim 5, wherein said reaction model further comprisesa second processor having an input connected to the output of saidsecond integrator of said reaction model, and having an output, whereinsaid second processor converts the reaction model heat feedforwardsignal into a signal indicative of a degree of the polymerizationprocess of the process in said reactor.
 7. A batch polymerizationprocess control device for controlling a batch process in a reactor,comprising:a first summer for receiving a reaction model heat feedbacksignal and a predetermined reaction heat signal and outputting a heatdifference signal; a second summer for receiving a process temperaturesignal from said reactor and a predetermined process temperature signaland outputting a process temperature difference signal; a controller forreceiving the heat difference signal and the process temperaturedifference signal and providing a dosing signal and reactor coolingcontrol signals to said reactor; and an inferential sensor, connected tosaid reactor and to said controller, for receiving parameter signalsfrom the reactor, providing a reaction model heat feedback signal tosaid controller, and receiving the reactor cooling control signals fromsaid controller.
 8. The batch polymerization process control device ofclaim 7, wherein said inferential sensor comprises:a reactor modelwherein said reactor model receives some parameter signals from saidreactor and the reactor cooling control signals from said controller andoutputs a signal indicating total heat removed from said reactor; and areaction model for receiving the signal indicating the total heatremoved from said reactor and providing the reaction model heat feedbacksignal to said first summer and to said reactor model.
 9. The batchpolymerization process control device of claim 8 inferential sensorfurther comprising a coordinator for receiving a reaction modeltemperature signal from said reaction model and the process temperaturesignal from said reactor, coordinating corresponding states of activityand simulated activity of said reactor and said reactor model,respectively, and outputting a coordinating signal.
 10. The batchpolymerization process control device of claim 9, wherein said reactionmodel comprises:a combiner for receiving the signal indicating the totalheat removed from said reactor and the coordinating signal, andproviding an output; a scale factor adjuster having an input connectedto the output of said combiner, and having an output; a first integratorhaving an input connected to the output of said scale factor adjuster,and having an output that provides the reaction model temperature signalto said reactor model and to said coordinator; a first processor forreceiving the dosing signal from said controller, having an inputconnected to the output of said first integrator, and having an outputfor providing a rate of reaction model heat production signal to saidcombiner; and a second integrator having an input connected to theoutput of said first processor and having an output for providing thereaction model heat feedback signal to said first summer, to saidreactor model, and to the input of said first processor.
 11. The batchpolymerization process control device of claim 10, wherein said reactionmodel further comprises a second processor having an input connected tothe output of said second integrator of said reaction model, and havingan output, wherein said second processor converts the reaction modelheat feedback signal into a signal indicative of a degree ofpolymerization of the batch process in said reactor.